\documentclass[9pt]{article}
\usepackage{amsmath}
\begin{document}
Read in the following dictionary:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  3.0 & +  9.00 x_{1} & +  6.00 x_{2} & +  6.00 x_{3} & +  1.00 x_{4} & -3.00 x_{5} & -7.00 x_{6} & -8.00 x_{7} & -1.00 x_{8} & +  2.00 x_{9}\\
 x_{11}   &  1.0 & +  9.00 x_{1} & -7.00 x_{2} & -3.00 x_{3} & -3.00 x_{4} &   & +  2.00 x_{6} & +  5.00 x_{7} & +  5.00 x_{8} & +  4.00 x_{9}\\
 x_{12}   &  3.0 & +  9.00 x_{1} & + 10.00 x_{2} & -9.00 x_{3} & -7.00 x_{4} & -4.00 x_{5} & +  7.00 x_{6} & -5.00 x_{7} & -4.00 x_{8} & +  5.00 x_{9}\\
 x_{13}   &  -2.0 & +  1.00 x_{1} & +  9.00 x_{2} & +  6.00 x_{3} & + 10.00 x_{4} & -3.00 x_{5} & -1.00 x_{6} & -6.00 x_{7} & -3.00 x_{8} & -8.00 x_{9}\\
 x_{14}   &  0.0 & -8.00 x_{1} & -9.00 x_{2} & -5.00 x_{3} & -7.00 x_{4} & -4.00 x_{5} & +  1.00 x_{6} & -7.00 x_{7} & +  7.00 x_{8} & +  4.00 x_{9}\\
 x_{15}   &  -2.0 & -5.00 x_{1} & + 10.00 x_{2} & +  9.00 x_{3} & -4.00 x_{4} & +  7.00 x_{5} & +  7.00 x_{6} & +  1.00 x_{7} & -5.00 x_{8} & +  6.00 x_{9}\\
 x_{16}   &  3.0 & -9.00 x_{1} & +  7.00 x_{2} & +  6.00 x_{3} & -6.00 x_{4} & -6.00 x_{5} & +  2.00 x_{6} & + 10.00 x_{7} &   & -2.00 x_{9}\\
 x_{17}   &  0.0 & -8.00 x_{1} & +  1.00 x_{2} & + 10.00 x_{3} & -7.00 x_{4} & -7.00 x_{5} & -4.00 x_{6} & -3.00 x_{7} & +  2.00 x_{8} & -2.00 x_{9}\\
 x_{18}   &  -2.0 & +  5.00 x_{1} & -5.00 x_{2} & + 10.00 x_{3} & -4.00 x_{4} & +  8.00 x_{5} & +  3.00 x_{6} & +  7.00 x_{7} & +  5.00 x_{8} & +  5.00 x_{9}\\
\hline
z    &  0.0 & -1.00 x_{1} & -3.00 x_{2} & -1.00 x_{3} & -1.00 x_{4} & +  2.00 x_{5} & -2.00 x_{6} & +  4.00 x_{7} & +  3.00 x_{8} & +  4.00 x_{9}\\
\end{array}\]
\subsection{Initialization Phase: Dual Problem Solving}
New Objective in primal was changed to : \[ \max\ \sum_{j=1}^{9}\ - x_j \] 
Primal variable $x_j$ corresponds to dual variable $y_j$ for $j = 1,\ldots,18$
Dual Dictionary (with objective changed is): 
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{1}   &  1.0 & -9.00 y_{10} & -9.00 y_{11} & -9.00 y_{12} & -1.00 y_{13} & +  8.00 y_{14} & +  5.00 y_{15} & +  9.00 y_{16} & +  8.00 y_{17} & -5.00 y_{18}\\
 y_{2}   &  1.0 & -6.00 y_{10} & +  7.00 y_{11} & -10.00 y_{12} & -9.00 y_{13} & +  9.00 y_{14} & -10.00 y_{15} & -7.00 y_{16} & -1.00 y_{17} & +  5.00 y_{18}\\
 y_{3}   &  1.0 & -6.00 y_{10} & +  3.00 y_{11} & +  9.00 y_{12} & -6.00 y_{13} & +  5.00 y_{14} & -9.00 y_{15} & -6.00 y_{16} & -10.00 y_{17} & -10.00 y_{18}\\
 y_{4}   &  1.0 & -1.00 y_{10} & +  3.00 y_{11} & +  7.00 y_{12} & -10.00 y_{13} & +  7.00 y_{14} & +  4.00 y_{15} & +  6.00 y_{16} & +  7.00 y_{17} & +  4.00 y_{18}\\
 y_{5}   &  1.0 & +  3.00 y_{10} &   & +  4.00 y_{12} & +  3.00 y_{13} & +  4.00 y_{14} & -7.00 y_{15} & +  6.00 y_{16} & +  7.00 y_{17} & -8.00 y_{18}\\
 y_{6}   &  1.0 & +  7.00 y_{10} & -2.00 y_{11} & -7.00 y_{12} & +  1.00 y_{13} & -1.00 y_{14} & -7.00 y_{15} & -2.00 y_{16} & +  4.00 y_{17} & -3.00 y_{18}\\
 y_{7}   &  1.0 & +  8.00 y_{10} & -5.00 y_{11} & +  5.00 y_{12} & +  6.00 y_{13} & +  7.00 y_{14} & -1.00 y_{15} & -10.00 y_{16} & +  3.00 y_{17} & -7.00 y_{18}\\
 y_{8}   &  1.0 & +  1.00 y_{10} & -5.00 y_{11} & +  4.00 y_{12} & +  3.00 y_{13} & -7.00 y_{14} & +  5.00 y_{15} &   & -2.00 y_{17} & -5.00 y_{18}\\
 y_{9}   &  1.0 & -2.00 y_{10} & -4.00 y_{11} & -5.00 y_{12} & +  8.00 y_{13} & -4.00 y_{14} & -6.00 y_{15} & +  2.00 y_{16} & +  2.00 y_{17} & -5.00 y_{18}\\
\hline
z    &  -0 & -3.00 y_{10} & -1.00 y_{11} & -3.00 y_{12} & +  2.00 y_{13} &   & +  2.00 y_{15} & -3.00 y_{16} &   & +  2.00 y_{18}\\
\end{array}\]
Initialization succeeded in finding final dual dictionary with 5 pivots
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{1}   &  3.73475416755 & -14.72 y_{10} & -14.12 y_{11} & -0.38 y_{2} & +  0.46 y_{4} & -1.86 y_{8} & -0.96 y_{3} & -2.19 y_{16} & -8.90 y_{17} & -23.80 y_{18}\\
 y_{12}   &  0.0116058240135 & +  0.03 y_{10} & +  0.08 y_{11} & -0.05 y_{2} & +  0.01 y_{4} & -0.02 y_{8} & +  0.05 y_{3} & -0.12 y_{16} & +  0.36 y_{17} & +  0.65 y_{18}\\
 y_{15}   &  0.0654146444398 & -0.49 y_{10} & +  0.10 y_{11} & -0.03 y_{2} & +  0.06 y_{4} & -0.03 y_{8} & -0.07 y_{3} & -0.96 y_{16} & -1.17 y_{17} & -0.89 y_{18}\\
 y_{13}   &  0.388056552015 & -0.60 y_{10} & -0.03 y_{11} & -0.12 y_{2} & -0.05 y_{4} & -0.21 y_{8} & -0.00 y_{3} & -0.58 y_{16} & -0.22 y_{17} & -0.27 y_{18}\\
 y_{5}   &  3.20278539776 & +  2.97 y_{10} & -2.90 y_{11} & -0.79 y_{2} & -0.42 y_{4} & -1.59 y_{8} & +  0.59 y_{3} & +  6.51 y_{16} & + 11.89 y_{17} & -4.36 y_{18}\\
 y_{6}   &  0.486389533657 & + 10.14 y_{10} & -2.67 y_{11} & +  0.57 y_{2} & -0.56 y_{4} & +  0.39 y_{8} & +  0.12 y_{3} & +  6.04 y_{16} & + 10.44 y_{17} & -0.47 y_{18}\\
 y_{7}   &  5.85861996202 & +  1.88 y_{10} & -9.18 y_{11} & -1.71 y_{2} & -0.13 y_{4} & -3.20 y_{8} & +  0.18 y_{3} & -20.14 y_{16} & -2.45 y_{17} & -12.17 y_{18}\\
 y_{14}   &  0.362523739185 & -0.45 y_{10} & -0.61 y_{11} & -0.10 y_{2} & +  0.03 y_{4} & -0.26 y_{8} & -0.02 y_{3} & -1.01 y_{16} & -1.01 y_{17} & -1.10 y_{18}\\
 y_{9}   &  2.20384047267 & -2.12 y_{10} & -2.80 y_{11} & -0.12 y_{2} & -0.92 y_{4} & -0.36 y_{8} & +  0.19 y_{3} & +  7.82 y_{16} & +  9.46 y_{17} & -0.67 y_{18}\\
\hline
z    &  0.872124920869 & -5.26 y_{10} & -1.12 y_{11} & -0.14 y_{2} & -0.02 y_{4} & -0.41 y_{8} & -0.30 y_{3} & -5.71 y_{16} & -3.85 y_{17} & -2.27 y_{18}\\
\end{array}\]
Primal Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  5.25849335303 & + 14.72 x_{1} & -0.03 x_{12} & +  0.49 x_{15} & +  0.60 x_{13} & -2.97 x_{5} & -10.14 x_{6} & -1.88 x_{7} & +  0.45 x_{14} & +  2.12 x_{9}\\
 x_{11}   &  1.11795737497 & + 14.12 x_{1} & -0.08 x_{12} & -0.10 x_{15} & +  0.03 x_{13} & +  2.90 x_{5} & +  2.67 x_{6} & +  9.18 x_{7} & +  0.61 x_{14} & +  2.80 x_{9}\\
 x_{2}   &  0.144650770205 & +  0.38 x_{1} & +  0.05 x_{12} & +  0.03 x_{15} & +  0.12 x_{13} & +  0.79 x_{5} & -0.57 x_{6} & +  1.71 x_{7} & +  0.10 x_{14} & +  0.12 x_{9}\\
 x_{4}   &  0.0150875712176 & -0.46 x_{1} & -0.01 x_{12} & -0.06 x_{15} & +  0.05 x_{13} & +  0.42 x_{5} & +  0.56 x_{6} & +  0.13 x_{7} & -0.03 x_{14} & +  0.92 x_{9}\\
 x_{8}   &  0.4141169023 & +  1.86 x_{1} & +  0.02 x_{12} & +  0.03 x_{15} & +  0.21 x_{13} & +  1.59 x_{5} & -0.39 x_{6} & +  3.20 x_{7} & +  0.26 x_{14} & +  0.36 x_{9}\\
 x_{3}   &  0.298269677147 & +  0.96 x_{1} & -0.05 x_{12} & +  0.07 x_{15} & +  0.00 x_{13} & -0.59 x_{5} & -0.12 x_{6} & -0.18 x_{7} & +  0.02 x_{14} & -0.19 x_{9}\\
 x_{16}   &  5.71164802701 & +  2.19 x_{1} & +  0.12 x_{12} & +  0.96 x_{15} & +  0.58 x_{13} & -6.51 x_{5} & -6.04 x_{6} & + 20.14 x_{7} & +  1.01 x_{14} & -7.82 x_{9}\\
 x_{17}   &  3.84996834775 & +  8.90 x_{1} & -0.36 x_{12} & +  1.17 x_{15} & +  0.22 x_{13} & -11.89 x_{5} & -10.44 x_{6} & +  2.45 x_{7} & +  1.01 x_{14} & -9.46 x_{9}\\
 x_{18}   &  2.26967714708 & + 23.80 x_{1} & -0.65 x_{12} & +  0.89 x_{15} & +  0.27 x_{13} & +  4.36 x_{5} & +  0.47 x_{6} & + 12.17 x_{7} & +  1.10 x_{14} & +  0.67 x_{9}\\
\hline
z    &  -0.872124920869 & -3.73 x_{1} & -0.01 x_{12} & -0.07 x_{15} & -0.39 x_{13} & -3.20 x_{5} & -0.49 x_{6} & -5.86 x_{7} & -0.36 x_{14} & -2.20 x_{9}\\
\end{array}\]
Primal Dictionary with original objective is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  5.25849335303 & + 14.72 x_{1} & -0.03 x_{12} & +  0.49 x_{15} & +  0.60 x_{13} & -2.97 x_{5} & -10.14 x_{6} & -1.88 x_{7} & +  0.45 x_{14} & +  2.12 x_{9}\\
 x_{11}   &  1.11795737497 & + 14.12 x_{1} & -0.08 x_{12} & -0.10 x_{15} & +  0.03 x_{13} & +  2.90 x_{5} & +  2.67 x_{6} & +  9.18 x_{7} & +  0.61 x_{14} & +  2.80 x_{9}\\
 x_{2}   &  0.144650770205 & +  0.38 x_{1} & +  0.05 x_{12} & +  0.03 x_{15} & +  0.12 x_{13} & +  0.79 x_{5} & -0.57 x_{6} & +  1.71 x_{7} & +  0.10 x_{14} & +  0.12 x_{9}\\
 x_{4}   &  0.0150875712176 & -0.46 x_{1} & -0.01 x_{12} & -0.06 x_{15} & +  0.05 x_{13} & +  0.42 x_{5} & +  0.56 x_{6} & +  0.13 x_{7} & -0.03 x_{14} & +  0.92 x_{9}\\
 x_{8}   &  0.4141169023 & +  1.86 x_{1} & +  0.02 x_{12} & +  0.03 x_{15} & +  0.21 x_{13} & +  1.59 x_{5} & -0.39 x_{6} & +  3.20 x_{7} & +  0.26 x_{14} & +  0.36 x_{9}\\
 x_{3}   &  0.298269677147 & +  0.96 x_{1} & -0.05 x_{12} & +  0.07 x_{15} & +  0.00 x_{13} & -0.59 x_{5} & -0.12 x_{6} & -0.18 x_{7} & +  0.02 x_{14} & -0.19 x_{9}\\
 x_{16}   &  5.71164802701 & +  2.19 x_{1} & +  0.12 x_{12} & +  0.96 x_{15} & +  0.58 x_{13} & -6.51 x_{5} & -6.04 x_{6} & + 20.14 x_{7} & +  1.01 x_{14} & -7.82 x_{9}\\
 x_{17}   &  3.84996834775 & +  8.90 x_{1} & -0.36 x_{12} & +  1.17 x_{15} & +  0.22 x_{13} & -11.89 x_{5} & -10.44 x_{6} & +  2.45 x_{7} & +  1.01 x_{14} & -9.46 x_{9}\\
 x_{18}   &  2.26967714708 & + 23.80 x_{1} & -0.65 x_{12} & +  0.89 x_{15} & +  0.27 x_{13} & +  4.36 x_{5} & +  0.47 x_{6} & + 12.17 x_{7} & +  1.10 x_{14} & +  0.67 x_{9}\\
\hline
z    &  0.495041147922 & +  2.93 x_{1} & -0.04 x_{12} & -0.02 x_{15} & +  0.21 x_{13} & +  4.55 x_{5} & -1.92 x_{6} & +  8.52 x_{7} & +  0.49 x_{14} & +  4.00 x_{9}\\
\end{array}\]
\section{Optimization Phase Simplex}
Starting Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  5.25849335303 & + 14.72 x_{1} & -0.03 x_{12} & +  0.49 x_{15} & +  0.60 x_{13} & -2.97 x_{5} & -10.14 x_{6} & -1.88 x_{7} & +  0.45 x_{14} & +  2.12 x_{9}\\
 x_{11}   &  1.11795737497 & + 14.12 x_{1} & -0.08 x_{12} & -0.10 x_{15} & +  0.03 x_{13} & +  2.90 x_{5} & +  2.67 x_{6} & +  9.18 x_{7} & +  0.61 x_{14} & +  2.80 x_{9}\\
 x_{2}   &  0.144650770205 & +  0.38 x_{1} & +  0.05 x_{12} & +  0.03 x_{15} & +  0.12 x_{13} & +  0.79 x_{5} & -0.57 x_{6} & +  1.71 x_{7} & +  0.10 x_{14} & +  0.12 x_{9}\\
 x_{4}   &  0.0150875712176 & -0.46 x_{1} & -0.01 x_{12} & -0.06 x_{15} & +  0.05 x_{13} & +  0.42 x_{5} & +  0.56 x_{6} & +  0.13 x_{7} & -0.03 x_{14} & +  0.92 x_{9}\\
 x_{8}   &  0.4141169023 & +  1.86 x_{1} & +  0.02 x_{12} & +  0.03 x_{15} & +  0.21 x_{13} & +  1.59 x_{5} & -0.39 x_{6} & +  3.20 x_{7} & +  0.26 x_{14} & +  0.36 x_{9}\\
 x_{3}   &  0.298269677147 & +  0.96 x_{1} & -0.05 x_{12} & +  0.07 x_{15} & +  0.00 x_{13} & -0.59 x_{5} & -0.12 x_{6} & -0.18 x_{7} & +  0.02 x_{14} & -0.19 x_{9}\\
 x_{16}   &  5.71164802701 & +  2.19 x_{1} & +  0.12 x_{12} & +  0.96 x_{15} & +  0.58 x_{13} & -6.51 x_{5} & -6.04 x_{6} & + 20.14 x_{7} & +  1.01 x_{14} & -7.82 x_{9}\\
 x_{17}   &  3.84996834775 & +  8.90 x_{1} & -0.36 x_{12} & +  1.17 x_{15} & +  0.22 x_{13} & -11.89 x_{5} & -10.44 x_{6} & +  2.45 x_{7} & +  1.01 x_{14} & -9.46 x_{9}\\
 x_{18}   &  2.26967714708 & + 23.80 x_{1} & -0.65 x_{12} & +  0.89 x_{15} & +  0.27 x_{13} & +  4.36 x_{5} & +  0.47 x_{6} & + 12.17 x_{7} & +  1.10 x_{14} & +  0.67 x_{9}\\
\hline
z    &  0.495041147922 & +  2.93 x_{1} & -0.04 x_{12} & -0.02 x_{15} & +  0.21 x_{13} & +  4.55 x_{5} & -1.92 x_{6} & +  8.52 x_{7} & +  0.49 x_{14} & +  4.00 x_{9}\\
\end{array}\]


 $ x_{1} $ enters and $ x_{4} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  5.73993595608 & -31.91 x_{4} & -0.36 x_{12} & -1.38 x_{15} & +  2.22 x_{13} & + 10.36 x_{5} & +  7.80 x_{6} & +  2.18 x_{7} & -0.39 x_{14} & + 31.37 x_{9}\\
 x_{11}   &  1.57982616651 & -30.61 x_{4} & -0.40 x_{12} & -1.90 x_{15} & +  1.59 x_{13} & + 15.68 x_{5} & + 19.88 x_{6} & + 13.07 x_{7} & -0.19 x_{14} & + 30.86 x_{9}\\
 x_{2}   &  0.157136322049 & -0.83 x_{4} & +  0.05 x_{12} & -0.02 x_{15} & +  0.16 x_{13} & +  1.14 x_{5} & -0.10 x_{6} & +  1.81 x_{7} & +  0.08 x_{14} & +  0.87 x_{9}\\
 x_{1}   &  0.0327081427264 & -2.17 x_{4} & -0.02 x_{12} & -0.13 x_{15} & +  0.11 x_{13} & +  0.91 x_{5} & +  1.22 x_{6} & +  0.28 x_{7} & -0.06 x_{14} & +  1.99 x_{9}\\
 x_{8}   &  0.47483989021 & -4.02 x_{4} & -0.02 x_{12} & -0.21 x_{15} & +  0.42 x_{13} & +  3.27 x_{5} & +  1.87 x_{6} & +  3.71 x_{7} & +  0.16 x_{14} & +  4.05 x_{9}\\
 x_{3}   &  0.329597438243 & -2.08 x_{4} & -0.07 x_{12} & -0.06 x_{15} & +  0.11 x_{13} & +  0.27 x_{5} & +  1.05 x_{6} & +  0.09 x_{7} & -0.04 x_{14} & +  1.71 x_{9}\\
 x_{16}   &  5.78316559927 & -4.74 x_{4} & +  0.07 x_{12} & +  0.69 x_{15} & +  0.82 x_{13} & -4.53 x_{5} & -3.37 x_{6} & + 20.74 x_{7} & +  0.88 x_{14} & -3.47 x_{9}\\
 x_{17}   &  4.14112534309 & -19.30 x_{4} & -0.56 x_{12} & +  0.03 x_{15} & +  1.20 x_{13} & -3.83 x_{5} & +  0.41 x_{6} & +  4.90 x_{7} & +  0.50 x_{14} & +  8.22 x_{9}\\
 x_{18}   &  3.04803293687 & -51.59 x_{4} & -1.19 x_{12} & -2.15 x_{15} & +  2.89 x_{13} & + 25.90 x_{5} & + 29.48 x_{6} & + 18.73 x_{7} & -0.26 x_{14} & + 47.95 x_{9}\\
\hline
z    &  0.590805123513 & -6.35 x_{4} & -0.10 x_{12} & -0.39 x_{15} & +  0.53 x_{13} & +  7.20 x_{5} & +  1.65 x_{6} & +  9.33 x_{7} & +  0.32 x_{14} & +  9.82 x_{9}\\
\end{array}\]


 $ x_{5} $ enters and $ x_{17} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  16.9398482767 & -84.10 x_{4} & -1.87 x_{12} & -1.30 x_{15} & +  5.47 x_{13} & -2.70 x_{17} & +  8.90 x_{6} & + 15.45 x_{7} & +  0.97 x_{14} & + 53.61 x_{9}\\
 x_{11}   &  18.5383788304 & -109.64 x_{4} & -2.69 x_{12} & -1.78 x_{15} & +  6.51 x_{13} & -4.10 x_{17} & + 21.54 x_{6} & + 33.15 x_{7} & +  1.87 x_{14} & + 64.54 x_{9}\\
 x_{2}   &  1.38826832328 & -6.56 x_{4} & -0.12 x_{12} & -0.01 x_{15} & +  0.52 x_{13} & -0.30 x_{17} & +  0.02 x_{6} & +  3.27 x_{7} & +  0.23 x_{14} & +  3.32 x_{9}\\
 x_{1}   &  1.01152858252 & -6.73 x_{4} & -0.15 x_{12} & -0.12 x_{15} & +  0.39 x_{13} & -0.24 x_{17} & +  1.31 x_{6} & +  1.43 x_{7} & +  0.06 x_{14} & +  3.93 x_{9}\\
 x_{8}   &  4.00621229317 & -20.48 x_{4} & -0.50 x_{12} & -0.18 x_{15} & +  1.44 x_{13} & -0.85 x_{17} & +  2.22 x_{6} & +  7.89 x_{7} & +  0.59 x_{14} & + 11.06 x_{9}\\
 x_{3}   &  0.626187205065 & -3.46 x_{4} & -0.11 x_{12} & -0.05 x_{15} & +  0.19 x_{13} & -0.07 x_{17} & +  1.08 x_{6} & +  0.44 x_{7} & +  0.00 x_{14} & +  2.30 x_{9}\\
 x_{16}   &  0.882384564841 & + 18.10 x_{4} & +  0.74 x_{12} & +  0.65 x_{15} & -0.61 x_{13} & +  1.18 x_{17} & -3.85 x_{6} & + 14.94 x_{7} & +  0.29 x_{14} & -13.21 x_{9}\\
 x_{5}   &  1.0814766143 & -5.04 x_{4} & -0.15 x_{12} & +  0.01 x_{15} & +  0.31 x_{13} & -0.26 x_{17} & +  0.11 x_{6} & +  1.28 x_{7} & +  0.13 x_{14} & +  2.15 x_{9}\\
 x_{18}   &  31.0610477271 & -182.13 x_{4} & -4.97 x_{12} & -1.94 x_{15} & + 11.02 x_{13} & -6.76 x_{17} & + 32.22 x_{6} & + 51.90 x_{7} & +  3.14 x_{14} & + 103.58 x_{9}\\
\hline
z    &  8.3790693507 & -42.64 x_{4} & -1.15 x_{12} & -0.33 x_{15} & +  2.79 x_{13} & -1.88 x_{17} & +  2.41 x_{6} & + 18.55 x_{7} & +  1.27 x_{14} & + 25.29 x_{9}\\
\end{array}\]


 $ x_{6} $ enters and $ x_{16} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  18.9762749686 & -42.33 x_{4} & -0.17 x_{12} & +  0.20 x_{15} & +  4.07 x_{13} & +  0.03 x_{17} & -2.31 x_{16} & + 49.93 x_{7} & +  1.63 x_{14} & + 23.13 x_{9}\\
 x_{11}   &  23.4698516992 & -8.50 x_{4} & +  1.42 x_{12} & +  1.86 x_{15} & +  3.12 x_{13} & +  2.52 x_{17} & -5.59 x_{16} & + 116.66 x_{7} & +  3.47 x_{14} & -9.26 x_{9}\\
 x_{2}   &  1.39249353024 & -6.48 x_{4} & -0.12 x_{12} & -0.01 x_{15} & +  0.52 x_{13} & -0.29 x_{17} & -0.00 x_{16} & +  3.34 x_{7} & +  0.23 x_{14} & +  3.26 x_{9}\\
 x_{1}   &  1.31251646495 & -0.56 x_{4} & +  0.10 x_{12} & +  0.10 x_{15} & +  0.19 x_{13} & +  0.17 x_{17} & -0.34 x_{16} & +  6.53 x_{7} & +  0.16 x_{14} & -0.57 x_{9}\\
 x_{8}   &  4.51355162635 & -10.08 x_{4} & -0.08 x_{12} & +  0.19 x_{15} & +  1.09 x_{13} & -0.17 x_{17} & -0.57 x_{16} & + 16.48 x_{7} & +  0.75 x_{14} & +  3.47 x_{9}\\
 x_{3}   &  0.87364212549 & +  1.62 x_{4} & +  0.09 x_{12} & +  0.13 x_{15} & +  0.02 x_{13} & +  0.26 x_{17} & -0.28 x_{16} & +  4.63 x_{7} & +  0.08 x_{14} & -1.40 x_{9}\\
 x_{6}   &  0.228913235499 & +  4.69 x_{4} & +  0.19 x_{12} & +  0.17 x_{15} & -0.16 x_{13} & +  0.31 x_{17} & -0.26 x_{16} & +  3.88 x_{7} & +  0.07 x_{14} & -3.43 x_{9}\\
 x_{5}   &  1.10574762517 & -4.54 x_{4} & -0.13 x_{12} & +  0.03 x_{15} & +  0.30 x_{13} & -0.23 x_{17} & -0.03 x_{16} & +  1.69 x_{7} & +  0.14 x_{14} & +  1.78 x_{9}\\
 x_{18}   &  38.4370147681 & -30.85 x_{4} & +  1.17 x_{12} & +  3.49 x_{15} & +  5.95 x_{13} & +  3.13 x_{17} & -8.36 x_{16} & + 176.80 x_{7} & +  5.53 x_{14} & -6.80 x_{9}\\
\hline
z    &  8.93068447723 & -31.33 x_{4} & -0.69 x_{12} & +  0.07 x_{15} & +  2.41 x_{13} & -1.14 x_{17} & -0.63 x_{16} & + 27.89 x_{7} & +  1.45 x_{14} & + 17.03 x_{9}\\
\end{array}\]


 $ x_{7} $ enters and Unbounded Dictionary!


 $ x_{7} $ enters and Unbounded Dictionary!
\end{document}
